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A mathematical model of pricing in a large system of cash bonds

Author

Listed:
  • F. Abikhalil
  • P. Dupont
  • J. Janssen
  • P. van Ossel

Abstract

The purpose of this paper is to give a mathematical model to generalize the classical approach of compound interest and to overcome the time structure problem of the interest rates. We introduce a suitable stochastic process called the ‘gauge’ process such that its product with the value of any security is assumed to be a martingale in an appropriate probability space. The framework of this model gives a stochastic actualization formula for the pricing of general securities with options and includes Black and Schole's formula without using arbitrage arguments. Emphasis has been placed on numerical calculation.

Suggested Citation

  • F. Abikhalil & P. Dupont & J. Janssen & P. van Ossel, 1985. "A mathematical model of pricing in a large system of cash bonds," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 1(1), pages 55-64.
    • Handle: RePEc:wly:apsmda:v:1:y:1985:i:1:p:55-64
    DOI: 10.1002/asm.3150010107
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